By Ed Belbruno
As an artist and mathematician, I have spent a lot of time trying to reconcile how I approach each of these two seemingly different things. When approaching a mathematical problem, it is necessary to abide by the process of deductive reasoning and physical laws. On the other hand, when I do a painting, these laws do not apply. In that case, it is necessary to allow the creative process to unfold in an unhindered manner as much as possible. However, these can synergize with one another in unexpected ways.
When starting a painting I am facing a blank canvas. Typically, I try to paint in an abstract expressionist manner. The canvas represents unlimited possibilities constrained only by its dimensions. Another constraint is the palette which dictates the range of colors. Also, when starting a painting, there is a conceptual idea of what will be represented, which is a fluid constraint. I try to free myself up enough so the unconscious can express itself as to how the piece will evolve. To facilitate the freedom of expression, I try to work fast with minimal thought. Minimizing the thought is a way to release control to the process. While the paint is being applied, one has another constraint that enters. That is to be mindful of the technical aspects of painting such as texture, composition, color. Most of the time, I am in the pure creative process where the subconscious can express itself as much as possible. The painting is done when it feels complete. This feeling of completion is subjective.
The process of doing a mathematics problem is much different. It isn’t done from a subjective perspective. For example, an area of mathematics I work in has to do with how objects like a spacecraft move in space, say from the Earth to the Moon. The mathematical equations governing the spacecraft motion takes into account the model of the Earth and Moon’s gravity. Since this motion can be chaotic in nature, laws of chaos theory need to be used. In solving the problem of finding a trajectory for a spacecraft to go from the Earth to the Moon, there are many steps. At each step, one has to insure the mathematical and physical relationships are satisfied. For example, knowing where the spacecraft is relative to the Earth and Moon, how fast it is going, and how to navigate with chaotic effects.
There is a clear goal in mind: making sure the spacecraft gets to the Moon to the desired location with enough fuel and within the required time. None of these considerations are subjective, unlike the artistic process. There is some free form creativity involved in how to approach the problem, but it usually lasts a very short amount of time, perhaps a few seconds. This is unlike the artistic process, where one needs to be in the creative mode most of the time.
The artistic and mathematical processes can yield a mysterious synergy. Once I found a new type of trajectory to the Moon, used to rescue a real spacecraft and getting it to the Moon. It was initially discovered in a painting I did. So, the art inspired mathematics. In the opposite sense, when my mathematics work focuses on random processes, as in my current work on the big bang in cosmology, the art process is freed up more, yielding new exciting artistic directions.